Senate leaders are working on a revised resolution authorizing U.S. strikes in Syria that puts President Barack Obama on a short leash in responding to the alleged use of chemical weapons by Bashar Assad’s forces, sources said Monday.

But whether Senate Majority Leader Harry Reid (D-Nev.) can find the 60 votes he will need to overcome an expected filibuster of the new Syria proposal is still far from clear.

Aides to Reid and Senate Foreign Relations Committee Chairman Robert Menendez (D-N.J.) have set aside a proposed Syria resolution submitted by the White House on Saturday night. That draft resolution — developed without congressional input — is seen as far too broad by lawmakers in both parties.

Sen. Bob Corker (R-Tenn.), ranking member on the Foreign Relations Committee, is also involved in the discussions over the new resolution, Senate sources said.

Some of the options being considered for the revised Authorization for the Use of Military Force include a 60-day period for Obama to launch “narrow, limited” strikes against Assad’s regime with the potential for a 30-day extension of that deadline.

Language barring the insertion of U.S. ground troops — but crafted to allow special forces operations or the rescue of a downed American flier, for instance — is also being considered, the sources said.

And Obama would be prohibited from making the toppling of Assad’s government the goal of any U.S. military effort in Syria, as some some hawkish lawmakers have supported.

The revisions are designed to win broad bipartisan backing from senators who are on the fence over whether to back a Syria campaign, GOP and Democratic sources said.

While the revised resolution has not been shared with them yet, White House aides say they are willing to work with Congress and believe it is likely that the edits put forward by Reid, Menendez and Corker are the kind of changes that the president will be able to live with.

When the new resolution will be unveiled and voted upon is unclear. Secretary of State John Kerry, Defense Secretary Chuck Hagel and other administration officials will be testifying on Tuesday before the Foreign Relations Committee in support of Obama’s call for a U.S. military response in Syria.

The panel has also scheduled a classified briefing for Wednesday. Senate aides said Foreign Relations could vote on the revised Syria resolution at that time, but whether that will actually happen is still up in the air.

Reid, though, wants the Syria measure on the Senate floor by next week knowing that it could take several days for the chamber to finish debating the hugely controversial issue.

Since Obama is going to Congress with a resolution authorizing the use of military force in Syria rather than ordering military strikes first and then informing Congress, as required under the War Powers Act, the use-of-force proposal will be fully debatable and amendable. Under the War Powers Act, a use-of-force resolution would face only limited debate and require a simple majority vote.

The revised proposal can be filibustered by those opposed to any U.S. involvement in Syria’s two-year-old civil war, meaning Reid will need 60 votes to overcome opposition to the measure. Some Senate Democrats, such as West Virginia Sen. Joe Manchin, have publicly stated that they do not support Obama’s position on Syria. With only 54 Senate Democratic votes to play with, Reid and the White House cannot afford many Democratic defections.

Top Senate Republicans, including Minority Leader Mitch McConnell and Minority Whip John Cornyn , have yet to say how they will vote. How many of the 46 Senate Republicans will vote for the Syria AUMF is difficult to estimate at this point. A Democratic aide suggested Reid and Obama “would be lucky” to get 10 to 15 Republican votes for the measure.

McConnell will take part in a broader meeting Tuesday at the White House that will also include Speaker John Boehner (R-Ohio), House Minority Leader Nancy Pelosi (D-Calif.) and the chairmen and ranking members of the House and Senate armed services, foreign relations and intelligence committees. Reid will not be attending that session.

Corker and Arizona Sen. John McCain, who serves on Foreign Relations, have been the most vocal Senate GOP supporters of Obama’s call for intervention in Syria.

In a statement released Monday, Corker called on Obama to “immediately use every resource appropriate in making his case to the public before this potentially defining vote in Congress.”

McCain, for his part, declared that it would be “catastrophic” if a use-of-force resolution against Syria fails to pass Congress.

“A rejection of this resolution would be catastrophic not just for him but for the institution of the presidency and the credibility of the United States,” McCain told reporters following a closed-door meeting on Monday with Obama at the White House. Sen. Lindsey Graham (R-S.C.) also took part in that session with the president.

Yet McCain said he isn’t convinced enough lawmakers support the Syria proposal because Obama has yet to outline his plan of attack against the Assad regime.

“I’m already talking to a lot of my colleagues, but before I can persuade them to support this, I have to be persuaded,” McCain said. “I’m saying that I think the president made sense in a lot of things he had to say, but we are a long way from achieving what I think would be a most effective strategy.”